Archive for August, 2010

The Duality of Time and Information

August 26, 2010

The states of a computing system bear information and change time, while its events bear time and change information.

from The Duality of Time and Information by Vaughn Pratt

The most promising transformational logic seems to us to be Girard’s linear logic.

— from Rational Mechanics and Natural Mathematics by Vaughn Pratt

References:

Vaughan Pratt / The Duality of Time and Information http://boole.stanford.edu/pub/dti.pdf

Vaughan Pratt / Time and Information in Sequential and Concurrent Computation http://boole.stanford.edu/pub/tppp.pdf

Vaughan Pratt / Rational Mechanics and Natural Mathematics http://chu.stanford.edu/guide.html#ratmech

 [*5.170]

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Aristotle’s Four Causes

August 12, 2010

Material: That from which something is made.

Efficient: That by which something is made.

Formal: That into which something is made.

Final: That for the sake of which something is made.

— from Aristotle for Everybody by Mortimer Adler

“Happy is he who can recognize the causes of things.”

Virgil

Aristotle’s Four Causes is likely the most familiar of all the double duals that I will present. The causes are closer to being “becauses” since they are usually thought of as the reasons or explanations for things. Why not call them the four prepositions?

The standard example of the four causes is what is needed for the building of a house. A house is built by the craftsmen, from the raw materials, into the form shown on blueprints, for the homeowner to live in. This and other usual examples are concerned with the making of something.

Formal and final causes have gotten the short shift since the beginning of the scientific revolution. Francis Bacon stated that the only scientific reasons for things were the efficient and material causes. For those critical of materialism this is often termed mere “matter in motion”. Matter can be thought to exist in space, and motion in time. Where does form or finality exist? I will say in space and time as well.

References:

Max Hocutt / Aristotle’s Four Becauses, in Philosophy, Vol. 49, No. 190. (Oct., 1974), pp. 385-399.

http://en.wikipedia.org/wiki/Four_causes

http://plato.stanford.edu/entries/aristotle-causality/

http://en.wikipedia.org/wiki/The_purpose_of_a_system_is_what_it_does

Notes:

John Sowa’s Thematic Roles: initiator, resource, essence, goal.

http://www.jfsowa.com/ontology/thematic.htm

[*4.112, *5.162, *5.168, *7.47]

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The Here and the Now

August 11, 2010

Whosoever speculated on these four things, it were better for him if he had not come into the world —

  • what is above?
  • what is beneath?
  • what was beforetime?
  • and what will be hereafter?

— From the Mishnah (Hagigah 2:1)

All things have a root and a top; all events an end and a beginning. Whoever understands correctly what comes first and what follows draws nearer the Dao.

— From T’ai Hioh by Confucius

As above, so below.

— From The Emerald Tablet

I like these quotes because they show that Above, Below, Before and After are linked together. The first quote gives a warning about thinking about these concepts, but the second, encouragement. Above and below, or higher and lower, can be thought of as directions in space, but also as terms of hierarchy. Before and after can be thought of as directions in time, but also as beginnings and endings, causes and results.

Every individual is situated in space and time (see SpaceTime). Every perspective is due to expression and content (see Hjelmslev’s Net). Here is space, now is time.

References:

http://en.wikipedia.org/wiki/Emerald_Tablet

[*5.160, *6.30]

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